Abstract: Regarding the characteristics of gear vibration, a compound over-complete time-frequency dictionary was designed. Basis pursuit, which is effective in matching the characteristic structure of signals globally and extracting the time-frequency information directly, was employed to analyze the vibration signals of both a healthy gearbox and a faulty one. Periodic impacts characterizing the vibration of localized damaged gears were extracted in the joint time-frequency domain, and gear tooth pitting was identified. In comparison with traditional time-frequency analysis methods, such as short time Fourier transform and wavelet transform, basis pursuit is effective in detecting gear damage.